In this paper we apply the lattice KMC coarse-graining framework proposed recently by Vlachos and coworkers [1,2] to a model for vacancy aggregation in crystalline silicon. The underlying microscopic KMC model is based on a bond counting approach with long-range interactions [3,4]. The bond energies are computed using a global regression approach in which the KMC model output is compared to molecular dynamics-generated data. We have shown previously that this approach allows us to capture off-lattice configurational entropic effects that substantially alter the evolution dynamics at the elevated temperatures relevant to point defect aggregation in crystalline semiconductors.
Several mean-field approximations and the quasi-chemical approximation are used to compute averaged KMC potentials for the coarse-grained systems. The application of these strategies to coarse-graining in the diamond lattice is investigated in detail and the different closure rules are compared and contrasted. We also study the application of coarse-graining to complex KMC interactions. The KMC interaction model in refs. [3,4] includes screening effects in which particles can obstruct bonding interactions between other pairs, effectively leading to a many-body potential. We begin by considering simplified interaction models and then investigate coarse-graining approaches to correctly capture the screening (many-body) component of our microscopic KMC potential.
 M. A. Katsoulakis and D. G. Vlachos, Coarse-grained stochastic processes and kinetic Monte Carlo simulations for the diffusion of interacting particles. J. Chem. Phys., 119 (2003) 9412.  A. Chatterjee and D. G. Vlachos, Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules. J. Chem. Phys., 121 (2004) 11420.  J. Dai, J. M. Kanter, S. S. Kapur, W. D. Seider and T. Sinno, On-lattice kinetic Monte Carlo simulations of point defect aggregation in entropically influenced crystalline systems. Phys. Rev. B, 72 (2005) 134102.